I understand how principal component analysis works. However, in a financial time series sense, I do not understand why the number of observations should be larger than the number of dimensions. I am having twenty securities (dimensions in this case) for ten time periods and I am told that PCA won't work here. Why wouldn't it work? Also, how does asymptotic principal component analysis help to solve this problem?
Can someone please explain this? If possible try to use less mathematical jargon (except for linear algebra basics such as eigenvalues/vectors). If it is not possible to explain it without using jargon, please go ahead and I will take my time and try to understand it.